Wallace wanted to avoid any confrontation with any magicians specializing with the Soul Art.
First, he was already aware of his soul's abnormality due to the Cube's arrangement when he set foot on this world.
Next, he had been using his Divine Sense that is probably a technique unique to their path. This might cause some complication if it was confirmed by the instructors and learned by his parents. After all, he won't be able to explain the origin of his Soul Arts.
Lastly, people who trained in Soul Arts were somehow capable of affecting someone's mind. Wallace wasn't exactly sure how they were doing it but he had seen and experienced it before.
It happened first when he met Miya at the Red Star Town together with his family. After that incident, he had his Avalon research about the Celebrity Idols and he found out that there was an unpopular article about them telling that these idols can make mental suggestions to any person within a limited range.
*Chapter 105 has the full description of the Fervor Timepiece.
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